Cartesian parametrization: where is the unique polynomial (called "Lagrange polynomial") of degree £
n satisfying where is an increasing sequence of real numbers.The interpolation is said to be "uniform" if the are equal, and "proportional to the chords" if the are proportional to the lengths .

Given a broken line (called control polygon, the Ak being the control points, the associated interpolating Lagrange curves are the polynomial curves of degree less than or equal to n passing through the points in that order.

Opposite, in green the uniform interpolation, and in red the interpolation proportional to the chords (closer to the control polygon).